Theoretical work is proposed in four areas: 1. Dilute Polymer Solutions, 2. Concentrated Polymer Solutions and Orientational Order in Liquids, 3. Imperfections and Anharmonicity in Solids, 4. Diffusion in Liquids. The equilibrium and nonequilibrium statistical mechanics of these systems will be studied with respect to specific problems. Examples are: The conformational statistics of short polymer chains, the mechanical and dielectric relaxation of polymers, orientational order in concentrated polymer solutions, interaction between imperfections in solids, diffusion toward imperfections.